My question is this: If two sets are equal does that mean that they are necessarily equal?

Answer 1

To supplement bobpursley's previous comment,
HUH ?

Answer 2

I suppose you mean to say:
"My question is this: If two sets are equal does that mean that they are necessarily equivalent?"
The answer is yes. Can you explain to us why this is so?
(Study Bob's previous statements to help you answer why)